Identify 19th term of a geometric sequence where a1 = 14 and a9 = 358.80

Marilyn Cameron

Marilyn Cameron

Answered question

2022-10-24

Identify 19th term of a geometric sequence where a1 = 14 and a9 = 358.80

Answer & Explanation

scranna0o

scranna0o

Beginner2022-10-25Added 16 answers

The general term of a Geometric Sequence is given by
a n = a r n - 1
Where a is the first term also known as a 1 and r is the common ratio.
We have a 1 if we get r we can easily find a 19 by using 19 for n
Let us start by writing the given term using r
a 9 = a r 8
If we divide a 9 by a 1 we would get an equation in r
a r 8 a = 358.80 14
r 8 = 25.628571428571428571428571428571
Taking 8th root.
r = 25.628571428571428571428571428571 8
#r=1.4999975504465127405341330547934"
r 1.5
a 19 = 14 ( 1.5 ) 19
a 19 = 31 , 035.729480743408203125
a 19 31035.73

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